Series: Mathematics Colloquium

Date: Thursday, February 13, 2003

Time: 4:30 - 5:30 PM

Place: 102 McAllister Building

Host: Luen-Chau Li

Refreshments: 4:00 - 4:30 PM, in 212 McAllister

Speaker: Nicolai Reshetikhin, Berkeley

Title: Local Geometry of Random 3D Young Diagrams

Abstract:

Three dimensional Young diagrams can be identified with plane
partitions, or with dimer configurations on a hexagonal lattice. The
probabilistic measure $q^V$ where $V$ is the volume of the diagram and
$q<1$ defines a natural statistic of such diagrams. It is known that
as $q\to 1$ the diagrams distributed with such measure develop a
limiting shape (Cerf and Kenyon).  I will show how representation
theory of $gl_\infty$ can be used to find the limiting shape of the
diagram and to compute correlation functions in this system.